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Difficulty: Very hardChaining Conditional Statements

The Faculty Research Committee has instituted the following rigid guidelines for grant allocations:
- A grant is approved for full funding only if the proposed project promises immediate commercial viability.
- Projects utilizing human subjects are invariably classified as High-Risk endeavors.
- Any project that is cleared by the Central Ethics Board necessarily incorporates multi-year longitudinal phases.
- Promising immediate commercial viability is impossible for any project that incorporates multi-year longitudinal phases.
- A project is classified as a High-Risk endeavor only when it is cleared by the Central Ethics Board.

Dr. Vance's proposed research project was just approved for full funding. Arrange the following logical deductions in the strictly required sequential order to construct a valid chain of inferences proving that Dr. Vance's project does not utilize human subjects.

  1. 1Deduce that the project promises immediate commercial viability, since this is a necessary condition for its newly approved full funding.
  2. 2Establish that the project cannot incorporate multi-year longitudinal phases, given its promise of immediate commercial viability.
  3. 3Conclude that the project lacks clearance from the Central Ethics Board, utilizing the contrapositive of the board's phase incorporation requirement.
  4. 4Determine that the project is not a High-Risk endeavor, because it lacks the Central Ethics Board clearance required for such a classification.
  5. 5Prove that the project does not utilize human subjects, since utilizing them would necessitate the High-Risk classification that the project lacks.

Answer

The correct sequence starts by deducing commercial viability from the funding approval, then the absence of longitudinal phases, followed by the lack of board clearance, then the lack of High-Risk classification, and finally concluding that human subjects are not utilized.
A valid logical deduction must proceed step-by-step from known facts. The known starting point is that the project received full funding (FF). First, the rule 'full funding only if... promises immediate commercial viability' translates to FF -> CV, yielding CV (item_cv). Second, the rule 'immediate commercial viability is impossible for any project that incorporates multi-year longitudinal phases' translates to MYL -> ~CV, and its contrapositive is CV -> ~MYL, yielding ~MYL (item_myl). Third, the rule 'cleared by the Central Ethics Board necessarily incorporates multi-year longitudinal phases' translates to CEB -> MYL, with the contrapositive ~MYL -> ~CEB, yielding ~CEB (item_ceb). Fourth, the rule 'High-Risk endeavor only when it is cleared by the Central Ethics Board' translates to HR -> CEB, with the contrapositive ~CEB -> ~HR, yielding ~HR (item_hr). Finally, the rule 'utilizing human subjects are invariably classified as High-Risk' translates to HS -> HR, with the contrapositive ~HR -> ~HS, proving the project does not use human subjects (item_hs).

Step-by-Step Solution

1
Translate the five policy rules into conditional statements.
1. FF -> CV; 2. HS -> HR; 3. CEB -> MYL; 4. MYL -> ~CV; 5. HR -> CEB.
Formalizing the statements prevents misinterpretation of necessary and sufficient conditions.
2
Identify the known starting fact regarding Dr. Vance's project.
The project has been approved for full funding (FF).
A valid deductive chain must begin with an established premise.
3
Chain the conditionals using modus ponens and contrapositives to reach the target conclusion (~HS).
FF -> CV -> ~MYL -> ~CEB -> ~HR -> ~HS.
This maps the exact logical progression required to prove the project does not utilize human subjects.
4
Match the formalized logical chain to the descriptive textual steps provided.
The correct order is item_cv, item_myl, item_ceb, item_hr, item_hs.
Each descriptive step explicitly relies on the conclusion generated by the immediately preceding logical step.

Key Concept

Chaining Conditional Statements and Contrapositives
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Topics

Chaining Conditional Statements

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